Question

the regular nonagon has rotational symmetry of which angle measures? check all that apply. 40° 45° 120° 240° 260° 320°

Explanation:

Step1: Calculate the smallest rotation angle

For a regular \(n -\)gon, the smallest angle of rotational symmetry is \(\frac{360^{\circ}}{n}\). A nonagon has \(n = 9\), so \(\frac{360^{\circ}}{9}=40^{\circ}\).

Step2: Find other rotation angles

The angles of rotational symmetry of a regular nonagon are multiples of \(40^{\circ}\).

• For \(k = 3\): \(k\times40^{\circ}=3\times40^{\circ} = 120^{\circ}\)
• For \(k = 6\): \(k\times40^{\circ}=6\times40^{\circ}=240^{\circ}\)
• For \(k = 8\): \(k\times40^{\circ}=8\times40^{\circ}=320^{\circ}\)

Answer:

\(40^{\circ}\), \(120^{\circ}\), \(240^{\circ}\), \(320^{\circ}\)